This is just something really simple about the award ceremony in the last episode. It takes place right before Jim confronts Gray in the garden.
ABSENCE MAKES THE HEART GROW FONDER
Gray was used to great amounts of discomfort in life. He knew how it was when there hadn't been enough to eat in weeks and what it felt like to get a knife wound running down his leg. He had fought in war and been both the patient and the one to hold the patient down when a doctor worked to remove a musket ball from a wound. The latter was something he had always found especially difficult to bear, but at that very moment he would have gladly endured it if it meant he could have escaped his current torment.
The jacket he was wearing was too hot, and the collar felt too tight and ticklish. He hadn't known what to do with his bowtie and probably wouldn't have worn it at all if Dr. Livesey hadn't been kind enough to show him how to tie it. That had been the moment when the adventure had ended for him.
Livesey had smiled as he had explained the intricacies of the garment. He hadn't meant to, of course, but he had made Gray feel like an ill-mannered fool. They had fought side by side and looked death in the eyes on the island, but it was all over now. They were no longer equals; they were back in the real world where doctors, squires and captains weren't friends with people like him.
Gray was certain that he was the only one who had realised it. The others were still too excited about the treasure and their warm welcome in Bristol. However, time would bring their differences to light. It wasn't just that Gray had never worn a bowtie before. He could barely read or write. He wouldn't know how to behave if Trelawney ever invited him for tea or some brandy. He understood nothing of the world in which the others lived.
Jim and Hunter would have it easier. They didn't belong to the upper class either, but they both held values and ambitions that society accepted. Out of everyone, only Ben Gunn was in the same situation as him, but the old pirate was eager to start a new life and didn't share Gray's cynicism despite the ten long years on the island.
Gray didn't want to learn to live in this world which wouldn't accept him as he was. He had to leave before the others noticed that they were too different.
"...and have I already told you how I survived the rain season six years ago when my cave became flooded? No? Then you must listen; it's a really great story!"
Gray smiled as he overheard Ben Gunn telling the journalists about his life on the island. Even though they had all nearly died there, he found himself already missing the place. Everything there had been so simple. Only the battle for life had mattered, and everyone's life had been equal no matter what rank, title or education they had. That was how Gray wanted to live.
He caught a glimpse of Smollett's stern face as the captain answered the journalists' questions with brief but precise accounts of their journey. Gray knew that Smollett or any of the others meant no harm and would never turn their backs on him. They just couldn't change the way society worked, so everything would inevitably become awkward between them. It was better if he left now before that happened. That way, everyone could think fondly back to their shared adventures and recall only how they had worked together at the fort, attacked the pirates and found the treasure – not how he couldn't tie a bowtie without help, had nothing to say when Livesey made a comment about some book he had recently read or how there was uncomfortable silence or even arguments when the conversation turned to Ireland.
Once he was sure that everyone's attention was elsewhere, Gray took a servants' entrance that led him to the garden. The fresh air tasted wonderful, and he let out a sigh of relief when he could finally tear the dreadful bowtie off and throw it to the ground with the rest of the unnecessary clothes – and the medal from the king, which he wasn't planning to keep.
He would miss the others, especially Jim. The boy was still so young and sincere. Just like he had found it difficult to accept that Silver was a terrible pirate and a good man at the same time, he would have a hard time understanding why Gray didn't feel at home with the rest of them.
Just because he was leaving like this didn't mean he never wanted to see the others again. It was the exact opposite. He would be more than happy to cross paths with all of them in the future. They could have a drink together, talk about their adventures and exaggerate their heroics. Then they'd part ways again before anything complicated came up.
Gray picked up his supplies and turned to go. He had kept his musket from Treasure Island as a memento. It would be his companion from now on and remind him of the adventures on the island until the day he met his friends again.